Space-time block code (STBC) design for wireless fading channels has been an area of recent research. As a result, several STBCs (e.g., orthogonal designs and linear dispersion (LD) codes) have been developed. Algebraic number theoretic tools for code design have also been employed for the independent and identically distributed (i.i.d.) Rayleigh fading model with success. Additionally, the real-baseband model has been used to show that all STBCs are lattice codes. This reveals that the traditional STBC design.
where input information symbols are drawn from quadrature amplitude modulation (QAM) constellations or pulse amplitude modulation (PAM) constellations result in lattice codes with sub-optimum (in terms of energy efficiency) shaping regions. Thus, a need exists to further improve performance by designing lattice codes with optimized shaping regions.
Though it may be beneficial to fix input information
symbols to be QAM symbols as this results in efficient maximum-likelihood (ML) decoding via the sphere decoder, the complexity of ML decoding can significantly increase for lattice codes with optimized shaping due to the problem of boundary control. One conventional way to balance this tradeoff is to employ sub-optimum decoders, which avoid boundary control and the increase in complexity, to decode optimized lattice codes.
Thus, there is a need to design optimal (in terms of error-rate) lattice codes for multiple-input multiple-output (MIMO) systems where the receiver employs lattice or lattice-reduction aided decoders. No such systematic design procedure has been previously proposed.